The field from an SH-point source in a continuously layered inhomogeneous medium: I. The field in a layer of finite depth

Expressions are derived for the field from an SH point source in a stratified heterogeneous layer of finite depth. It is found, that for a periodic disturbance, the contribution to the far field is mainly due to at most a finite number of unattenuated normal Love modes. The transient response of the medium is obtained by a Fourier synthesis. The final expressions are of a simple form, involving the eigenfunctions of a Sturm-Liouville boundary value problem. The excitation of a certain mode as a function of frequency and source depth is formulated in a concise form.